Reforming Geometry

Visual reasoning is central to mathematics. It is an integral part of mathematical and scientific inquiry. Geometry also has another aspect that it shares with the broader field of mathematics—its potential use for modeling situations. Because of this aspect, geometry should—those who seek a reformed school mathematics curriculum claim—be integrated into the mathematics courses children study throughout their K-12 years. The NCTM Standards (1989) and other reform documents (MSEB, 1989; MSEB, 1990) call for increased content in geometry and spatial reasoning across Grades K-4, 5-8, and 9-12. Geometry, a course devoted to visually guided thought, is taught to students in the United States at the 10 th grade level. Most elementary school curricula cover the descriptive aspects of geometry briefly. Students learn to identify and name conventional shapes in elementary and middle school grades. Their 10 th-grade course is built around twocolumn proofs of theorems in Euclidean geometry. Current instructional practice isolates the content of geometry from the content of other mathematical areas, a practice that begins with algebra in 8 th-or 9 th-grade classrooms. A discussion of algebra is carried in the Winter 1993 issues of the NCRMSE Research Review. The isolation of geometri